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We compute the renormalization of dimension six Higgs-gauge boson operatorsthat can modify \Gamma(h -> \gamma \gamma) at tree-level. Operator mixing isshown to lead to an important modification of new physics effects which hasbeen neglected in past calculations. We also find that the usual formula forthe S oblique parameter contribution of these Higgs-gauge boson operators needsadditional terms to be consistent with renormalization group evolution. Westudy the implications of our results for Higgs phenomenology and for newphysics models which attempt to explain a deviation in \Gamma(h -> \gamma\gamma). We derive a new relation between the S parameter and the \Gamma(h ->\gamma \gamma) and \Gamma(h ->Z \gamma) decay rates.

Renormalization Group Scaling of Higgs Operators and \Gamma(h -> \gamma \gamma)